{
  "id": 406,
  "curve_key": "1012668051784204689475435281:-31984196471620625894576090709919170535929",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-21097251078837597697404902",
    "37018745916232850579640184758127094901"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 186.5471579824078,
  "faltings_height": 13.398354364729014,
  "conductor": "2644553355450364179430274416851803216811334386659749432662237930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "47",
    "3264101",
    "982147597",
    "1233077721715118924761",
    "5453598607079233734187"
  ],
  "discriminant": "8969214692406883015730398815550145450361500168920974846388502144587468800000",
  "regulator": "9383778911288440110.1357955156395791959854566005916675790171404039597616127",
  "points": [
    [
      "774954654401",
      "4597252669544889099"
    ],
    [
      "12998944309897769/12769",
      "-5878204090838967977438997/1442897"
    ],
    [
      "173463963061750709/61009",
      "-2078635754840004602860623/15069223"
    ],
    [
      "-39670626660931/121",
      "-8818854028811383937979/1331"
    ],
    [
      "3528660775209957061/938961",
      "-2991316092457691829405345509/909853209"
    ],
    [
      "937634068670048801/63001",
      "868947381915949154789355249/15813251"
    ],
    [
      "238100297958593141/96721",
      "1124136951756921055763889/30080231"
    ],
    [
      "8629332410790761/961",
      "712256125210844543384709/29791"
    ],
    [
      "4550481028769441/1849",
      "-4611156367817102527647/79507"
    ],
    [
      "-2669533887520471/529",
      "-47079725558352391977267/12167"
    ],
    [
      "2644115007895631489/466489",
      "-3178782620894868414475633887/318611987"
    ],
    [
      "1882793609828342609/635209",
      "367307169483188807749466727/506261573"
    ],
    [
      "32009748639641",
      "-179331156600287048181"
    ],
    [
      "1972047015990865511/383161",
      "1908806134510994025910543041/237176659"
    ],
    [
      "14666508037349599411/86436",
      "-56147778119232515764106975909/25412184"
    ],
    [
      "1982097829371409/9",
      "88225452343984517038073/27"
    ],
    [
      "14529639536122041/5041",
      "-141029179945811070820211/357911"
    ],
    [
      "84290081689321481/25921",
      "6983190880364833683634779/4173281"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "commentary": "Rank-18 curve from Mestre's quartic construction, specialized at T = 2357/2. The sextuple is [0, 113, 550, 753, 868, 1058], the canonical primitive representative from u = -3, v = -1/2 in the Mestre-Fermigier family, whose generic member has rank 12.",
  "created_at": "2026-08-28 20:29:07",
  "updated_at": "2026-08-28 20:29:07"
}